Problem
A company is producing a new product. Due to the nature $K \quad$ of the product, the time required to produce each unit decreases as workers become more familiar with the production procedure. It is determined that the function for the learning process is $T(x)=1+0.6\left(\frac{1}{x}\right)$, where $T(x)$ is the time, in hours, required to produce the xth unit. Find the total time required for a new worker to produce units 1 through 5 ; units 20 through 25. The Tworker requires $\square$ hours to produce units 1 through 5 . (Round to two decimal places as needed.)
Solution
Step 1 ：The problem is asking for the total time required for a new worker to produce units 1 through 5. This can be calculated by summing up the time required to produce each unit from 1 to 5 using the given function \(T(x)=1+0.6\left(\frac{1}{x}\right)\).
Step 2 ：By substituting the values of x from 1 to 5 into the function, we get the total time required to produce units 1 through 5.
Step 3 ：The total time required is approximately 6.37 hours.
Step 4 ：Final Answer: The worker requires \(\boxed{6.37}\) hours to produce units 1 through 5.
